We study the influence of taking liquidity costs and market impact into account when hedging a contingent claim, first in the discrete time setting, then in continuous time. In the latter case and in a complete market, we derive a fully non-linear pricing partial differential equation, and...

We consider a multi-asset continuous-time model of a financial market with transaction costs and prove that, for a strongly risk-averse investor, the reservation price of a contingent claim approaches the super-replication price increased by the liquidation value of the initial endowment....

We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we allow for nonsmooth utility functions, so as to include the...

In this paper, we prove a multidimensional extension of the so-called Bipolar Theorem proved in Brannath and Schachermayer (Séminaire de Probabilités, vol. XXX, 1999, p. 349), which says that the bipolar of a convex set of positive random variables is equal to its closed, solid convex hull....

We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in...

We consider a general multivariate financial market with transaction costs as in Kabanov and we analyse the stochastic control problems of maximizing the expected utility of the liquidation value of terminal wealth diminished by some random claim G for a utility function of exponential form.

We consider a singular version with state constraints of the stochastic target problems studied in Soner and Touzi (SIAM J. Control Optim. 41:404–424, <CitationRef CitationID="CR23">2002</CitationRef>; J. Eur. Math. Soc. 4:201–236, <CitationRef CitationID="CR24">2002</CitationRef>) and more recently Bouchard et al. (SIAM J. Control Optim. 48:3123–3150, <CitationRef CitationID="CR6">2009</CitationRef>), among others....</citationref></citationref></citationref>

Motivated by an optimal investment problem under time horizon uncertainty and when default may occur, we study a general structure for an incomplete semimartingale model extending the classical terminal wealth utility maximization problem. This modelling leads to the formulation of a wealth-path...

We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transactions is used to obtain a tractable model. A...

Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward numerical scheme for the Fenchel transform of the pricing function. This algorithm is similar to the...